Week - 1 - Consistency of Units

Aim:- To understand the unit system and be conversant with converting quantities from one system of units to another. Because LS-DYNA doesn't have any default system of the unit.

Objective:-

• convert the given quantities with the given unit system.
• calculate and mention the conversion factors.
• crate the table with the measuring unit.

conversion of given quantities SI unit to gm/mm/ms unit system

• MASS 1kg = 1000g=`10^3` or `e^3`gram

conversion factor:- `10^3`

• LENGTH 1m = 1000mm= `10^3` or `e^3`mm

conversion factor:- `10^3`

• TIME 1s = 1000ms =`10^3` or `e^3`ms

conversion factor:- `10^3`

• FORCE 1N = 1 `(kgxxm)/s^2`

= 1`(1000gmxx1000mm)/(1000ms)`

= 1 `(1gmxxmm)/(ms)`

conversion factor:- 1

• STRESS 1Pa = 1`N/m^2`

= `{(kgxxm)/(s^2)/m^2}`

= `{(1000gmxx1000mm)/(1000000ms^2)`/1000000`mm^2`}`

=(`10^2`gm mm)/`10^6``mm^2`

=(1gm mm)/`ms^2`/`10^6 mm^2`

=`10^-6`gm/mm `ms^2`

conversion factor:- `10^-6`

• ENERGY 1Nm = `{1(kgxxm)/(s^2)}xxm`

= `{1(1000gmxx1000mm)/(1000ms)^2}xx1000mm`

=`{1(10^6gmxxmm)/(10^6ms^2)}xx10^3mm`

=`{(1gmxxmm)/(ms^2)}xx10^3mm`

=`10^3(gmxxmm^2)/(ms^2`

conversion factor:- `10^3`

• DENSITY `1(Kg)/m^3`= `(1000gm)/(1000mm)^3`

= `(10^3gm)/(10^9mm^3)`

= `(10^-6gm)/(mm^3)`

conversion factor:- `10^-6`

• YOUNG'S Modulus 210GPa =`210xx1000N/(mm^2`

=`210xx1000(kgxxm)/s^2/mm^2`

=`{210xx1000(1000gmxx1000mm)/(1000ms)^2}/(mm^2)`

=`{210xx10^3(1gmxxmm)/(mm^2)}/(mm^2)`

=`210xx10^3gm/(mmxxms^2`

conversion factor:- `10^3`

• Velocity 56.33KMPH = `(56.33xx1000mm)/H`

=`(56.33xx10^6mm)/(3600xx1000ms`

=`(56.33xx10^6mm)/(36xx10^5ms`

=`15.6472(mm)/(ms`

conversion factor:- 0.27778`(mm)/(ms`

• GRAVITY 9.8`m/s^2`= `9.8(1000mm)/(1000ms)^2`

= `9.8(10^3mm)/(10^6ms^2`

= `9.8xx10^-3(mm)/(ms^2`

conversion factor:- `10^-3`

Measuered unit table as follow:-

S.I unites	Mass	Length	TIME	FORCE	STRESS	ENERGY	DENSITY	YOUNG'S Modulus	VELOCITY 56.33	GRAVITY 9.8
Kg cm ms	1kg	10^2cm	10^3ms	10^-4kg*cm/ms^2	10^-8kg/cm*ms^2	10^-2kg*cm^2/ms^2	10^-6kg/cm^3	2100kg/cm*ms^2	1.56472cm/ms	9.8*10^-4cm/m^2
Kg cm s	1kg	10^2cm	1s	10^2kg*cm/s^2	10^-3kg/cm*s^2	10^4kg*cm^2/s^2	10^-6kg/cm^3	210e^7kg/cm*s^2	1564 cm/s	9.8*10^2cm/s^2
g mm ms	10^3gm	10^3mm	10^3ms	1g*mm/ms^2	10^-6g/ms^2mm	10^3g*mm2/ms^2	10^-6g?mm^2	210*10^3g/ms^2mm	15.64mm/ms	9.8*10^-3mm/ms ^2
kg m s	1kg	1m	1s	1kg*m/s^2	1pa=kg/m*s^2	1Nm=1J=kg*m^2/s^2	kg?m^3	210e^9kg/m s^2	15.64m/s	9.8m/s^2
g cm s	10^3gm	10^2cm	1s	10^5g*cm/s^2	10g/cm*s^2	10^6g*cm^2/s^2	10^-3g/CM^3	2.1*10^12g/cm*s^2	1564 cm/s	9.8*10^2 cm/s^2
g cm us	10^3gm	10^2cm	10^6us	10^-7g*cm/us^2	10^-11g/cm*us^2	10^-5g*cm^2/us^2	10^-3g/CM^3	2.1g/cm*us^2	15.6*10^-4cm/us	9.8*10^-10cm/us^2
g mm s	10^3gm	10^3mm	1s	10^6g*mm/s^2	1g/mm*s^2	10^9g*mm^2/s^2	10^-3g/CM^3	2.1*10^11g/mm*s^2	1564mm/s	9.8*10^3mm/s^2
ton mm s	10^-3t	10^3mm	1s	1t*mm/s^2	10^-6t*mm/s^2	10^3t*mm^2/s^2	10^-12t/mm^3	210*10^3 t*mm/s^2	1564mm/s	9.8*10^3mm/s^2
slug ft s	0.068slug	3.28ft	1s	0.2246slug/ft*s^2	0.0208slug*ft/s^2	0.7366slug*ft^2/s	1.93*10^-3ft^3	4.368e^9slug*ft/s^2	51.32ft/s	32.144ft/s^2
kg mm s	1kg	10^3mm	1s	10^3kg*mm/s^2	10^-3kg/mm*s^2	10^6kg*mm^2/s^2	10^-9kg/mm^3	2.1*10^8kg/mm*s^2	1564mm/s	9.8*10^3mm/s^2
g cm ms	10^3gm	10^2cm	10^3ms	10^-1g*cm/ms^2	10^-5g/cm*ms^2	10g*cm^2/ms^2	10^-3g/CM^3	2.1*10^6g/cm*ms^2	1.56cm/ms	9.8*10^-4 cm/ms^2
kg mm ms	1kg	10^3mm	10^3ms	10^3kg*mm/ms^2	10^-9kg/mm*ms^2	1kg*mm^2/ms^2	10^-9kg/mm^3	2.1*10^2kg/mm*ms^2	15.64mm/ms	9.8*10^-3mm/ms^2

conversion factor table is as follow:-

S.I unites	Mass	Length	TIME	FORCE	STRESS	ENERGY	DENSITY	YOUNG'S Modulus	VELOCITY 56.33	GRAVITY 9.8
Kg cm ms	1	10^2	10^3	10^-4	10^-8	10^-3	10^-6	10	1	10^-4
Kg cm s	1	10^2	1	10^2	10^-3	10^4	10^-6	10^7	1	10^2
g mm ms	10^3	10^3	10^3	1	10^-6	10^3	10^-6	10^3	1	10^-3
kg m s	1	1	1	1	1	1	1	10^9	1	1
g cm s	10^3	10^2	1	10^5	10	10^6	10^-3	10^12	1	10^2
g cm us	10^3	10^2	10^6	10^-7	10^-11	10^-5	10^-3	1	10^-4	10^-10
g mm s	10^3	10^3	1	10^6	1	10^9	10^-6	10^11	1	10^3
ton mm s	10^-3	10^3	1	1	10^-6	10^3	10^-12	10^3	1	10^3
slug ft s	0.068	3.28	1	1	1	1	10^-3	10^9	1	1
kg mm s	1	10^3	1	10^3	10^-3	10^6	10^-9	10^8	1	10^3
g cm ms	10^3	10^2	10^3	10^-1	10^-5	10	10^-3	10^6	1	10^-4
kg mm ms	1	10^3	10^3	10^-3	10^-9	1	10^-9	10^2	1	10^-3

Conclusion:-

• converted the given quantities within the required "SI" unit system.
• created the tables with the obtained result.